The Manchester City stopper is one of three goalkeepers in the provisional squad along with Robert Green and David James, but is considered third choice despite being named in the Premier League Team of the Year.
James is being rested against Mexico after featuring in the FA Cup final against Chelsea, meaning it is likely that the 23-year-old and Green will play 45 minutes each.
Speaking the the FA’s official website, Hart said: "It would mean everything to play at Wembley.
"I don't really think about it, plan for it or set any goals, because it is an absolute bonus just to be involved in the squads.”
Hart has impressed Fabio Capello following an excellent season on loan with Birmingham City and now has been recalled by Manchester City. But he hopes to impress further to obtain the No.1 jersey for his country.
"I will be doing everything in my power to catch the manager's eye and hopefully get a few more caps to my name,” he added.
Despite the competition between the three as to who will be first choice in South Africa, Hart says there is a good atmosphere in the camp.
"The spirit between the keepers is definitely there," he said. "We train and work together far more closely than anyone else in the squad.
"We are all different keepers and obviously Jamo and Greeny have got vast experience over me which I am looking to learn off.
"They are two big personalities and great people to be around."
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